The above bivariate distribution is a special case of Cheriyan and Ramabhadran's bivariate gamma distribution (see [1]}). Here random variable \(X_i\)  follows Gamma distribution with pdf \(f_i(\frac{x}{\theta _i})=\frac{x}{\theta _i^2}\,e^{-\frac{x}{\theta _i}},\; x>0\) , \(i=1,2\) .
For estimation of \(\theta _i\) , consider the squared error loss function
\( L_i(\underline{\theta },a)=\left(\frac{a}{\theta _i}-1\right)^2\, , \; \underline{\theta }\in \Theta _0,\;a\in \Re _{++},\;i=1,2.\) 
